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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.06919 |
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| _version_ | 1866929666907963392 |
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| author | Moreno, Agustin Limoge, Arthur |
| author_facet | Moreno, Agustin Limoge, Arthur |
| contents | In arXiv:2011.06562, the first author and Otto van Koert proved a generalized version of the classical Poincaré-Birkhoff theorem, for Liouville domains of any dimension. In this article, we prove a relative version for Lagrangians with Legendrian boundary. This gives interior chords of arbitrary large length, provided the twist condition introduced in arXiv:2011.06562 is satisfied. The motivation comes from finding spatial consecutive collision orbits of arbitrary large length in the spatial circular restricted three-body problem, which are relevant for gravitational assist in the context of orbital mechanics. This is an application of a local version of wrapped Floer homology, which we introduce as the open string analogue of local Floer homology for closed strings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_06919 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Relative Poincaré-Birkhoff theorem Moreno, Agustin Limoge, Arthur Symplectic Geometry In arXiv:2011.06562, the first author and Otto van Koert proved a generalized version of the classical Poincaré-Birkhoff theorem, for Liouville domains of any dimension. In this article, we prove a relative version for Lagrangians with Legendrian boundary. This gives interior chords of arbitrary large length, provided the twist condition introduced in arXiv:2011.06562 is satisfied. The motivation comes from finding spatial consecutive collision orbits of arbitrary large length in the spatial circular restricted three-body problem, which are relevant for gravitational assist in the context of orbital mechanics. This is an application of a local version of wrapped Floer homology, which we introduce as the open string analogue of local Floer homology for closed strings. |
| title | A Relative Poincaré-Birkhoff theorem |
| topic | Symplectic Geometry |
| url | https://arxiv.org/abs/2408.06919 |